1. 8-4 Area of Parallelograms Course 2 Warm Up Problem of the Day Lesson Presentation

2. Warm Up Find each product. 1. 8  12 2. 3 3. 9.4  6.3 4. 3.5  7 96 59.22 Course 2 8-4 Area of Parallelograms 1212  5 1313 18 2323 24.5

3. Problem of the Day How many 3 ft by 2 ft rectangles can you cut from one 8 ft by 4 ft rectangle? How much will be left over? 5 pieces; 2 ft 2 left over Course 2 8-4 Area of Parallelograms

4. Learn to find the area of rectangles and other parallelograms. Course 2 8-4 Area of Parallelograms

5. Vocabulary area Insert Lesson Title Here Course 2 8-4 Area of Parallelograms

6. Course 2 8-4 Area of Parallelograms The area of a figure is the number of unit squares needed to cover the figure. Area is measured in square units. AREA OF A RECTANGLE The area A of a rectangle is the product of its length l and its width w. A = lw w l

7. Find the area of the rectangle. Additional Example 1: Finding the Area of a Rectangle Course 2 8-4 Area of Parallelograms 4.5 in. 7.4 in. A = lw A = 7.4 · 4.5 A = 33.3 The area of the rectangle is 33.3 in 2. Use the formula. Substitute for l and w. Multiply.

8. Find the area of the rectangle. Course 2 8-4 Area of Parallelograms 6.3 in. 8.2 in. A = lw A = 8.2 · 6.3 A = 51.66 The area of the rectangle is 51.66 in 2. Use the formula. Substitute for l and w. Multiply. Try This: Example 1

9. Course 2 8-4 Area of Parallelograms For any parallelogram that is not a rectangle, you can cut a right triangle-shaped piece from one side and move it to the other side to form a rectangle. The base of a parallelogram is the length of one side. The height of a parallelogram is the perpendicular distance from the base to the opposite side. Base Height Base

10. Course 2 8-4 Area of Parallelograms The base of the parallelogram is the length of the rectangle. The height of the parallelogram is the width of the rectangle. Helpful Hint The area A of a parallelogram is the product of its base b and its height h. AREA OF A PARALLELOGRAM A = bh h b

11. Find the area of the parallelogram. Additional Example 2: Finding the Area of a Parallelogram Course 2 8-4 Area of Parallelograms 8 m 16 m A = bh A = 16 · 8 A = 128 The area of the parallelogram is 128 m 2.

12. Find the area of the parallelogram. Course 2 8-4 Area of Parallelograms 6 cm 12 cm A = bh A = 12 · 6 A = 72 The area of the parallelogram is 72 cm 2. Try This: Example 2

13. A carpenter is using 2-ft by 2-ft square tiles to cover a rectangular floor. If the area of the floor is 150 ft 2, what is the least number of tiles the carpenter will need? Additional Example 3: Measurement Application Course 2 8-4 Area of Parallelograms First find the area of each tile. A = lwUse the formula for the area of a square. A = 2 · 2 Substitute 2 for l and 2 for w. A = 4 Multiply. The area of each square tile is 4 ft 2.

14. Additional Example 3 Continued Course 2 8-4 Area of Parallelograms To find the number of tiles needed, divide the area of the floor by the area of one tile. 150 ft 2 4 ft 2 = 37.5 Since covering the floor requires more than 37 tiles, the carpenter would need at least 38 tiles.

15. Try This: Example 3 Insert Lesson Title Here Course 2 8-4 Area of parallelograms Amanda decided to use 1.5-ft by 1.5-ft square tiles to cover a rectangular floor. If the area of the floor is 200 ft 2, what is the least number of tiles Amanda will need? First find the area of each tile. A = lwUse the formula for the area of a square. A = 1.5 · 1.5 Substitute 1.5 for l and 1.5 for w. A = 2.25 Multiply. The area of each square tile is 2.25 ft 2.

16. Try This: Example 3 Continued Insert Lesson Title Here Course 2 8-4 Area of Parallelograms To find the number of tiles needed, divide the area of the floor by the area of one tile. 200 ft 2 2.25 ft 2 ≈ 88.9 Since covering the floor requires more than 88 tiles, Amanda would need at least 89 tiles.

17. Lesson Quiz: Part 1 Find the area of each figure. 1. 2. 3. 24.5 ft 2 Insert Lesson Title Here 84 ft 2 Course 2 8-4 Area of Parallelograms 3.5 ft 7 ft 2 1212 5 1414 12 ft 4 1212 6 1212 ft 4. 13 1818 in 2 105 8 or 28 1212 ft 2 57 2 or

18. Lesson Quiz: Part 2 5. Suzanne is planning to use 1 ft by 0.5 ft tiles to finish her bathroom floor. If her floor is 7 ft by 10 ft, how many tiles will she need? 140 tiles Insert Lesson Title Here Course 2 8-4 Area of Parallelogram